In computer programming, an algorithm is a methodically laid-out plan for completing a task. It takes in certain information and outputs the desired outcome. Since algorithms are typically created separately from their underlying languages, the same algorithm can be translated into many other languages.

### Qualities of a good algorithm

• Input and output must be defined precisely.
• Each step of the algorithm must be clear and unmistakable.
• An algorithm is the most effective method for solving a problem.
• Algorithms shouldn't involve computer code. Instead, the method should be built in a way that makes it portable across languages.

### How to write an algorithm

• There are no established standards for algorithm development. However, the difficulty of the task depends on the resources at hand. Algorithm development never takes any specific programming language into account.
• As you are all aware, all programming languages share flow control structures like if-else and other fundamental code components like loops like do, for, and while. These typical building blocks can be used to create an algorithm.
• Algorithms are typically constructed in a sequential fashion, but this is not always the case. Algorithm development starts with a precise definition of the problem space. That is to say, you should be familiar with the context in which the solution is being created.

### Analysis of an Algorithm

Both the input data and the output from the algorithm can be studied. The two algorithms are described below:

Priori analysis
Here, "a priori analysis" means judging an algorithm's efficacy on paper before actually using it. Variables like processing speed can be considered in advance of putting the method into practice.
Posterior analysis
In this context, a practical analysis of an algorithm is referred to as a posterior analysis. Any programming language can use the algorithm to carry out the experimental investigation. This evaluation establishes the required storage capacity and processing time.

### The Most Essential Algorithms for Programmers

Listed below are some of the famous algorithms that can help programmers produce effective and competent results.

• Binary search algorithm
When searching through ordered lists, binary search is the most efficient strategy. Before employing the binary search approach to locate an item in a list, we must ensure that the list is sorted.

By splitting the list into two parts and comparing the item with the middle element of the list, the divide and conquer method is used in binary search. If a match is made, the middle element's position is returned. If not, we conduct our search in either half based on the outcome of the match.

Breadth-first search (BFS) is a technique for traversing and searching through tree and graph data structures. It begins at the root of the tree (or any other random node in a graph; this is frequently referred to as the "search key") and initially looks at its neighbors before going on to its next-level neighbors.

The "breadth-first search" strategy for traversing graphs starts by checking out all of the neighboring nodes, then moves on to the root node. The next thing it does is pick the nearest node and check out all the unexplored ones. For the purposes of BFS traversal, any node in the graph can be considered the root node.

There are other techniques to navigate the graph; however, BFS is the method that is most frequently applied. The process of searching for every vertex in a tree or graph data structure is recursive. Using BFS, the graph's vertices are separated into two classes: visited and non-visited. A single node in a graph is chosen, and then all of the nodes next to that node are visited.

• Depth-first search
A method for exploring and traversing tree and graph data structures is called depth-first search (DFS). Starting at the root (choosing any node at random to serve as the graph's root), one must travel as far as possible along each branch before turning around.

The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.

• Merge sort algorithm
An effective sorting technique called merge sort creates a stable sort, which implies that if two elements have the same value, they retain their relative positions in the sorted sequence from the input. The sorted sequence preserves the relative order of elements with identical values. As a comparison sort, merge sort is able to sort any input for which a less-than relation is specified.

As a Divide and Conquer algorithm, merge sort is used. Merge sort, like all other divide-and-conquer algorithms, splits a huge array into two smaller subarrays before recursively sorting the smaller subarrays.

• Quick sort algorithm
When properly implemented, the quicksort in-place sorting algorithm typically outperforms merge sort and heapsort by a factor of two to three. Quicksort may sort items of any type for which a less-than relation is defined because it is a comparison sort. It is typically not a stable sort in efficient implementations.

In order to sort n objects, Quicksort typically performs O (n.log(n)) comparisons. Even though this is quite unusual, it still requires O (n2) comparisons at worst.

• Lee Algorithm: shortest path in a maze
Find the length of the shortest path from a starting point in a binary rectangular matrix labyrinth to an ending point in the maze.

Only cells with a value of 1 can be used to build the path, and there is a maximum of one step per turn in any of the four directions. Here are the legal options:

Go Top: (x, y) ——> (x – 1, y)
Go Left: (x, y) ——> (x, y – 1)
Go Down: (x, y) ——> (x + 1, y)
Go Right: (x, y) ——> (x, y + 1)

• Bellman-Ford Algorithm: Single Source Shortest Paths
Find the shortest path weight d(s, v) from a source vertex s in a set of vertices V in a weighted directed graph whose edge weights w(u, v) can be negative. Take note that the graph displays a negative-weight cycle. The Bellman-Ford approach is effective because it consistently underestimates the actual path length from the first vertex to all other vertices. Then, it iteratively finds paths that are shorter than the overestimated paths, therefore relaxing the estimations.

• Union-find Algorithm (disjoint-set data structure)
A disjoint set is a type of set data structure that maintains information on a set of elements that has been split into multiple, mutually exclusive subsets. No single element belongs to more than one of the sets that make up a disjoint set. Since it allows for union and finds operations on subsets, it is also referred to as a union-find data structure. Let's start with a definition:

The Find method locates an element within a set and returns the element's subset's representative. The term "representative" is frequently applied to one specific item in this set. Union: It combines two distinct groups into one, with the group's spokesperson switching roles.

MakeSet is another useful operation that may be performed on disjoint sets; it generates a set that contains only the specified element

• Insertion sort Algorithm
Insertion sort is a stable in-place sorting method because it creates the final sorted array one element at a time. Although it is not the most effective algorithm, it is more efficient in the classic sense than other O(n2) algorithms like selection sort and bubble sort. Hybrid sort, which combines several sorting algorithms, includes insertion sort as one of them.

Since it can sort a list as it gets it, it is also a popular online algorithm. In contrast to other algorithms, sorting algorithms require all input pieces before they can be used. However, an insertion sort permits us to begin with an already partially sorted set of components. Additional elements (the ones that weren't already in memory) can be inserted and sorted if desired. Real-world sorting tasks typically include dynamic rather than static data. Other algorithms don't react well if even a single element is added to the set during sorting. However, only the insertion sort algorithm remains unaffected and adapts well to the new data.

• Euclidean Algorithm
The Euclidean algorithm relies on the fact that replacing the larger integer with its difference with the smaller number does not alter the greatest common divisor of the two numbers.

Since the greater of the two numbers is decreased whenever this replacement is made, doing so repeatedly results in smaller pairs of numbers until the original numbers are once again equal. When it happens, the result is the GCD of the initial two digits.

• Boyer-Moore Majority Vote Algorithm
The method iteratively processes the sequence's elements. During X's processing,
1. If the counter is at 0, choose candidate x as the current one, and increment the counter by 1.
2. If the counter is already positive, you may use it to keep track of whether or not x is in the running by adding to or subtracting.
The algorithm will preserve the element at the end of this process in accordance with the majority vote of the sequence. If there isn't overwhelming support for one option, the algorithm could report the wrong answer. To restate, the correct outcomes can be expected from the Boyer-Moore majority vote technique if the majority element is present in the input.

• Quickselect Algorithm
An unordered list's kth smallest element can be located with the use of a selection process called Quickselect. Similar to Quicksort, which is another sorting method. Similar to Quicksort, it has strong average-case performance but subpar worst-case performance while still being efficient in the traditional sense. Similar to Quicksort, Quickselect employs a single element to act as a pivot and divides the data into two halves based on whether or not the value of that element is less than or larger than the pivot. However, unlike Quicksort, which recursively searches both sides, Quickselect only searches one side. Since the pivot has reached its final sorted location, everything before it and everything after it are also unsorted. As a result, the complexity goes from O(n.log(n)) to O(n) on average and O(n2) in the worst case, where n is the amount of the input.

• Heap Sort Algorithm
Heapsort is a sorting algorithm that performs in-place comparisons to sort data into sorted and unsorted regions. It is sometimes considered an enhanced version of selection sorting. By repeatedly taking the largest or smallest member and adding it to the sorted set, the unsorted set is shrunk. Instead of performing a linear-time search for the maximum, the new method employs a heap data structure. Since the implementation of Heapsort does not generate a stable sort, the input order of equal elements is not maintained in the sorted output. When compared to O (n.log n) sorting algorithms like quicksort and merge sort, it is noticeably slower.

• Counting Sort Algorithm
If you need to sort an array whose keys are all integers and fall within a certain range, you can use the counting sort technique. It determines where each key value should be placed in the output by first counting how many items have that particular key value.

Counting sort is an effective way to determine the most used letter in a file or to sort an array with a restricted range. Counting sort needs to be reliable because it is frequently used as a subroutine in the radix sorting algorithm.

The program iteratively processes the data, generating a histogram that shows how frequently each key appears in the input set. The output array's index, into which items with a given key begin, is then computed using a prefix sum operation. The last step is a second loop of the data, this time inserting the items into the output array in the order they were sorted.

### Conclusion

In order to solve a real-world problem, you need to break it down into manageable chunks, and in order to do that, you need to have a firm grasp on the theory behind the problem. However, as we all know, theory is incomplete without practice, and algorithms have both theoretical and practical importance. Selecting the proper data format is essential, but so is having a solid understanding of common methods. Here are some well-known algorithms that any aspiring computer programmer and IT major should be familiar with.